Why is the size of L1 cache smaller than that of the L2 cache in most of the processors ?
There are different reasons for that.
L2 exists in the system to speedup the case where there is a L1 cache miss. If the size of L1 was the same or bigger than the size of L2, then L2 could not accomodate for more cache lines than L1, and would not be able to deal with L1 cache misses. From the design/cost perspective, L1 cache is bound to the processor and faster than L2. The whole idea of caches is that you speed up access to the slower hardware by adding intermediate hardware that is more performing (and expensive) than the slowest hardware and yet cheaper than the faster hardware you have. Even if you decided to double the L1 cache, you would also increment L2, to speedup L1-cache misses.
So why is there L2 cache at all? Well, L1 cache is usually more performant and expensive to build, and it is bound to a single core. This means that increasing the L1 size by a fixed quantity will have that cost multiplied by 4 in a dual core processor, or by 8 in a quad core. L2 is usually shared by different cores --depending on the architecture it can be shared across a couple or all cores in the processor, so the cost of increasing L2 would be smaller even if the price of L1 and L2 were the same --which it is not.